Re: Another AppendTo replacement problem
- To: mathgroup at smc.vnet.net
- Subject: [mg118234] Re: Another AppendTo replacement problem
- From: Peter Pein <petsie at dordos.net>
- Date: Sun, 17 Apr 2011 07:54:12 -0400 (EDT)
- References: <iobuv2$bec$1@smc.vnet.net>
Am 16.04.2011 13:36, schrieb Iván Lazaro:
> Hi dear group!
>
> I've read multiple times in this forum about the slow performance of
> AppendTo with big lists. I have now a problem with it, but have not
> been able to replace it properly. This is a toy version of my problem.
> The code below have to be run multiple times, but it is really slow. I
> wonder if somebody have an idea about this AppendTo problem.
>
>
> NumBasis = 10000;
> q = matrA = ma = Table[0, {i, 2}];
> M = RandomComplex[{-1 - I, 1 + I}, {NumBasis, 2, 2}];
> M = Map[Orthogonalize, M];
> matr = RandomComplex[{-1 - I, 1 + I}, {2, 2}]
> Results = {};
>
> Do[{ma[[k]] =
> KroneckerProduct[M[[Nbase, k]], Conjugate[M[[Nbase, k]]]];
> matrA[[k]] = Chop[matr.ma[[k]]];
> matrA[[k]] = matrA[[k]]/Tr[matrA[[k]].matrA[[k]]] // Chop;
> If[k == 2,
> AppendTo[
> Results, {M[[Nbase]], Eigenvalues[matrA[[k]]], {k, 1, 2}}]];
> }, {Nbase, 1, NumBasis}, {k, 1, 2}];
>
> M = Sort[Results, #1[[2]]< #2[[2]]&][[1, 1]];
>
> Thanks in advance!.
>
Hi Iván,
there is no need to build a list while calculating, because there is
already M. With a few nested anonymous functions and heavy mapping:
NumBasis=10^4;
SeedRandom[1]; (* to make result comparable *)
matr=RandomComplex[{-1-I,1+I},{2,2}];
M=RandomComplex[{-1-I,1+I},{NumBasis,2,2}];
AbsoluteTiming[
M=Orthogonalize/@M;
First[Results=
SortBy[
Transpose[{M,
(Total[Eigenvalues[#1]]&) /@
Map[(#1/Tr[#1.#1]&)[matr.#1]&,
MapThread[KroneckerProduct,{M,Conjugate[M]},2],
{2}][[All,2]]
}],
Abs[#1[[2]]]&]
]
]
gives
{0.4700006,
{
{{ 0.552668 - 0.232809 I, -0.550734 - 0.58056 I},
{-0.760505 + 0.248977 I, -0.375566 - 0.467538 I}},
0.297748 + 0.654164 I
} }
hth,
Peter